|On the Semi-absoluteness of Isomorphisms between the Pro-$p$ Arithmetic Fundamental Groups of Smooth Varieties
étale fundamental group
p-adic local field
pro-p Grothendieck conjecture
|European Mathematical Society - EMS - Publishing House GmbH
|Publications of the Research Institute for Mathematical Sciences
|Let p be a prime number. In the present paper, we consider a certain pro-p analogue of the semi-absoluteness of isomorphisms between the étale fundamental groups of smooth varieties over p-adic local fields [i.e., finite extensions of the field of p-adic numbers ℚp] obtained by Mochizuki. This research was motivated by Higashiyama’s recent work on the pro-p analogue of the semi-absolute version of the Grothendieck conjecture for configuration spaces [of dimension ≥2] associated to hyperbolic curves over generalized sub-p-adic fields [i.e., subfields of finitely generated extensions of the completion of the maximal unramified extension of ℚp].
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